**Direct empirical status of theoretical symmetries in physics**

** Affiliations:** Université catholique de Louvain (UCLouvain), Faculté de philosophie, arts et lettres (FIAL); Université catholique de Louvain (UCLouvain), Institut supérieur de philosophie (ISP), Centre de philosophie des sciences et sociétés (CEFISES)

** Supervisor:** Alexandre Guay

** Funding:** PhD funding by FSR (Special Research Funds, UCLouvain and the French-speaking community of Belgium) as part of an FSR project of Alexandre Guay (2014/10/01-2018/09/30)

** Defence committee:** Guido Bacciagaluppi (UtrechtU), Simon Friederich (RUGroningen), Michel Ghins (UCLouvain), Alexandre Guay (UCLouvain), Jean-Michel Counet (UCLouvain)

** Public defence poster:** [pdf] (2019/05/27)

** Excerpt of the thesis:** [pdf] (comprises title pages, contents, acknowledgements, a brief summary and references)

** Institutional repository:** [link] (includes chapter summaries in English and French, as well as metadata)

*Abstract*

A theoretical symmetry is said to have* direct empirical status (DES)* when it is matched with an empirical symmetry in the world.

For instance, Galileo’s ship empirical symmetry consists in that experiments inside a ship look the same for an observer located within the ship whether it moves or not with respect to the shore. Other more or less* recognised empirical symmetries* are Faraday’s cage, ‘t Hooft’s beam-splitter and Einstein elevator empirical symmetries. These are usually matched with global theoretical symmetries constituted by boosts, electrostatic potential shifts, phase shifts and constant accelerations respectively and are not matched with local theoretical symmetries such as those constituted by electromagnetic potential transformations and diffeomorphisms. *The literature on DES* includes [Kosso 2000], [Brading and Brown 2004], [Healey 2009], [Greaves and Wallace 2014], [Friederich 2015] (all in the *BJPS*), [Teh 2016] and [Friederich 2017].

In the thesis I discuss the ontology of theoretical symmetries in physics in general, analyse the four first texts on DES and provide my own account of DES.

One feature of my account is the formalisation of at least* macroscopic empirical symmetries* as relational phenomena, i.e.as dependent on the choice of suitable references. I tell in the thesis how these references function and in particular when they have to change and when they have to stay invariant. Another feature of my approach is the distinction between a weaker DES and a stronger DES. These are* the observational DES*, which is a matching between observable features of empirical symmetries and observational consequences of theoretical symmetries, and* the ontological DES*, which is the observational DES plus a matching between the physical and the theoretical underpinnings of the features and of the consequences involved in the observational DES. I further defend what I call* the empirical approach*, i.e.the idea of establishing DES by asking which theoretical symmetries are able to adequately represent a given empirical symmetry. I show that it follows from the empirical approach that an infinity of theoretical symmetries have the observational DES with respect to a given instance of an empirical symmetry. Moreover, it also follows that all such matchings are mostly ensured not by theoretical transformations but by* theoretical states*, which in my account are more or less the same as models linked by a theoretical symmetry transformation.

In light of these results I then revisit the usual preference from the literature on DES for assigning DES to global symmetries alone. To do so I firstly determine which global/local distinction for transformations is potentially relevant in my context and next define a similar distinction for theoretical states. I then ask whether the amended traditional position is right by which only theoretical symmetries where theoretical transformations and states are global in all the relevant variables have the ontological DES. One way for this to be right is if there exists an empirical symmetry with respect to which only such fully global theoretical symmetries have the observational DES. However, I present* a proof* by which given a fully global theoretical symmetry with the latter DES with respect to some empirical symmetry one can always construct a fully local theoretical symmetry and a mixed theoretical symmetry with the same status with respect to the same empirical symmetry. To do so I use suitable* gauge symmetries* in the sense of theoretical symmetries constituted by transformations which do not bring about any change in observational consequences. Given also my critique of other arguments from the literature on DES I therefore conclude that* there is currently no reason whatsoever to hold that only global or fully global theoretical symmetries have the ontological DES.* I end up by showing that which theoretical symmetries have the ontological DES depends on the ontological status of gauge symmetries, where the latter are defined as above.